Intermediate Investments F3031 Spot Futures Parity How to value a futures contract (REVIEW) –Create two portfolios. In the first, buy the asset and then sell it Forward –In the second portfolio, invest the price of the asset in a risk free asset –Compare the payoffs of these two strategies. They should be equal –Use the price of the asset and the risk free rate to determine the value of the forward contract F = S 0 (1+r f ) - D t

Intermediate Investments F3032 What Are the Options When Purchasing an Asset? Buy and Store Take a Long Futures Position The cost of these two strategies ought to be equal!

Intermediate Investments F3033 The Two Strategies (cont) Strategy A –Buy at spot price S 0, and hold until time T when the Spot Price will be S T Strategy B –Take a Long Futures position and invest enough money to pay the futures price when the contract matures

Intermediate Investments F3034 The Two Strategies (cont)

Intermediate Investments F3035 The Two Strategies (cont) The Payoffs of both strategies is S T So -S 0 = -F 0 / (1 + r f ) T And F 0 = S 0 (1 + r f ) T

Intermediate Investments F3036 An Example of Spot-Futures Parity Suppose you are considering taking physical delivery of live cattle as part of a futures contract. The cost of carry is assessed at 4% relative to te current spot price for cattle of $100. If the contract has 2 months to maturity, what is the value of the futures contract and the up-front cost of storing and feeding the cattle for two months?

Intermediate Investments F3037 What if Dividends Are Involved? If dividends are involved, the Spot – futures parity equation is adjusted to: F 0 = S 0 (1 + r f – d) T Where d is the dividend yield

Intermediate Investments F3038 In Class Exercises A futures contract on the S&P500 index entitles the buyer to receive the cash value of the S&P500 index at the maturity date of the contract The buyer of the contract does not receive the dividends paid on the S&P500 during the contract life The price paid at the maturity date of the contract is determined at the time the contract is entered into – this is the futures price There are four delivery months in effect at any one time –March June SeptemberDecember The closing value of the index is based on the prices on the 3 rd Friday of each delivery month

Intermediate Investments F3039 In Class Exercises Assume the following: –Contract is for the S&P500 index –Traded on the Chicago Mercantile Exchange –Value is equal to $250 times the S&P500 index –Assume the closing price on 1/22/97 was –The yield on a T-Bill maturing in 26 weeks was 5.11% –Assume the annual dividend yield to be 1.1% per year –What was the futures price for contracts maturing in March, June, September and December –Days to maturity were 57, 148, 239 and 330 respectively

Intermediate Investments F30310 In Class Exercises Given the results of the previous exercise, assume –The observed price for the June 1997 futures contract was actually $820 –How could you profit from this discrepancy? –Which asset is overpriced relative to the other? –Remember the age old adage of investing that ALWAYS works…BUY LOW AND SELL HIGH!!!

Intermediate Investments F30311 How to Hedge Using S&P500 Futures Assume the following: –Suppose a portfolio manager hold a portfolio that exactly mimics the S&P500 index. The current value of this portfolio is $ million –The S&P500 index is currently at –The December S&P500 futures price is –How can the fund manager hedge against future price movements?

Intermediate Investments F30312 How to Hedge Using S&P500 Futures Fund manager would sell a futures contract at –This means he must deliver the index (which he holds) for 645. The manager has locked in a price What will the value of the portfolio be at the maturity date of the contract? How does this hedge the risk? REMEMBER: Whenever you hedge with a futures contract, you now have two distinct events. What happens to the contract and what happens to the asset. These events are distinct and offset each other!

Intermediate Investments F30313 How to Hedge Using S&P500 Futures Scenario 1: The stock market falls and the index is only at maturity Scenario 2: The stock market rises and the index is at at maturity